TABLE OF CONTENTS The first practical transformers appeared roughly 50 years after Faraday discovered his law of induction. A typical transformer consists of two coils that are inductively coupled. For greater flux coupling, the coils may be wound on a highly permeable core with ? r ? 10 4. Transformers can either convert high voltage low current to low voltage high current signals (step down) or vice versa (step up). Electrical power lines carry high AC voltage, low current electricity so as to minimize I 2 R Joule heating losses.
For an ideal transformer with primary and secondary turn numbers N p and N s, the AC voltages across the primary and secondary turns are related to the time rate of change of magnetic flux threading the coils V p = - N p ? ? / ?t and V s = - N s ? ?/ ?t. Since ? ?/ ?t is the same for both coils we have
| (6.106) |  |
The primary voltage is stepped down for V p > V s and stepped up for V p < V s. If there are no power losses, the input power is equal to the output I pV p = I sV s. Figure 6.17 shows a transformer simulation carried out in x-y symmetry. The primary coil is located on the right of this figure and the secondary...
